In the field of total shoulder prostheses, prostheses are commonly said to be inverted when they comprise, on the one hand, a glenoid part integral with the glenoid surface of a scapula of a patient's shoulder and delimiting a convex articular surface and, on the other hand, a humeral part integral with the humerus of the shoulder and delimiting a concave articular surface, the cooperation of these articular surfaces allowing an articulated connection to be reproduced at the shoulder. With this type of prosthesis, it is common, during adduction movement of the shoulder, for the lower portion of the humeral prosthetic part to strike the pillar of the scapula, i.e. the lower portion of the bone glenoid surface located, when the patient stands upright, just below the glenoid prosthetic part. This interference between the humeral prosthetic part and the scapula limits the range of the adduction movement and may cause pain to the patient or even lead to the prosthesis becoming dislodged, in particular by osteolysis of the scapula.